Question

The terms of a geometric sequence always increase? True or False. Please Explain!

Answer 1

increase because youre multiplying...

Answer 2

In a geometric sequence each new term is the previous term multiplied by a constant factor, right?

Answer 3

yes so it does increase true?

Answer 4

Let's say you start with 1, and the constant factor is 2, then you have:
1, 2, 4, 8, 16, 32, ...
Ok?

Answer 5

yes so you multiply the previous number by 2 to get to the next

Answer 6

Yes, in that case.
Now start a new sequence with 256, and use the constant ratio of 1/2 instead of 2. What will the next few terms be? In this case, you start with 256, and you divide each term by 2 to get the next term. What are the next few terms?

Answer 7

would that be 256, 128, 64, 32?

Answer 8

Exactly.
This is also a geometric sequence.
Are the terms increasing or decreasing?

Answer 9

oh it would be true. they are increasing because like the first one 1, 2, 4, 8, 16, 32, ... this would be 32, 64, 128, 256?

Answer 10

????
256, 128, 64, 32, ...
is not the same as 32, 64, 128, 256, ...
The order of the numbers matter.

Answer 11

oh ok so that one was decreasing

Answer 12

but wasn't the first one increasing

Answer 13

In the first example, 1, 2, 4, 8, 16, 32, ...
you had a geometric sequence with increasing terms.
In the second example, 256, 128, 64, 32, ...
you have a geometric sequence with decreasing terms.

Answer 14

That means terms in a geometric sequence may increase or decrease.
Now answer the original question.

Answer 15

Im starting to see for the sake of this question it is asking if the terms in geometric sequences ALWAYS increase which is not always the case so false then?

Answer 16

Exactly.